Apple Tarte Tatin

To make the crust: Use a food processor, mixer, or pastry blender/fork to blend together the flour, sugar, salt, and butter till the mixture has formed fine crumbs.
Add the egg yolk and water, mixing to make a firm, cohesive dough; add a bit more water if necessary.
Form the dough into a disk, wrap, and chill while preparing the filling.
To make the filling: Slice the butter into thin pats and use them to completely cover the bottom of a burner-safe, oven-safe 9" to 10" round pan, such as a cast iron skillet.
Sprinkle the sugar over the butter.
Arrange the apple slices in concentric circles in the pan, placing the nicest ones on the bottom; pack them in tightly so they all fit.
Place the pan on a burner, and cook over low to medium heat for 45 minutes to 1 hour, or until the butter and sugar have caramelized, and all the moisture from the apples has evaporated.
Remove from the heat, and drizzle with the boiled cider or apple juice concentrate.
While the apples are cooking, preheat the oven to 425F.
Roll the dough on a lightly floured surface to a 9" circle.
Place the dough over the apples, tucking the edges inside the pan.
Prick the pastry lid all over with a fork.
To bake the tarte: Bake the tarte tatin for 20 to 30 minutes, or until the crust is golden brown and crisp.
Remove from the oven, cool slightly, then run a spatula around the edge of the pan and invert onto a serving plate.
Serve warm or at room temperature.